I read the user's guide and it seems that MLR in Mplus 7 can handle both missing data and non-normal data. Am I correct? My understanding is that ML solution to missing data usually assumes a multivariate normal distribution. If MLR in Mplus can handle both missing data and non-normal data, does it mean that MLR, though still assumes multivariate normal distribution, makes some adjustments such that even though the distribution is not so normal, it's results are robust to the deviation? If I want to know how robust MLR as implemented in Mplus is, are there simulation studies on its performance when both missing data and non-normal data are present in a dataset, for various degrees of deviation from multivariate normal distribution? I would like to know to what extent I can trust the MLR results for my dataset. Thanks.

Missing data modeling does indeed assume normality. MLR robustness does not necessarily hold for the combination of missing data and non-normality. There have been simulation studies of this combination - see articles by Victoria Savalei in the SEM journal for instance (e.g. her 2010 article). See also Yuan et al (2012) in a recent issue of Sociological Methods & Research.

Thanks for your prompt reply and the references. I am studying them. I am also interested in the technical details. May I know whether the section on MLR in the following web note in 2002 on MLR is still relevant to the Mplus 7?

I am working on a paper examining longitudinal pathways predicting perpetration of dating violence in young adulthood. I'm using path analyses in mplus, accounting for the fact that dating violence is censored. There are three outliers in my dating violence variable. If I get rid of outliers (either by transforming or trimming), I get the same pattern of results regardless of whether I: (a) use MLR (even after transformation the variable has high kurtosis), (b) use ML without robust estimation, (c) don't account for censoring at all and just use ML. Thus, my results seem consistent. However, if I don't remove the outliers, and just use MLR to account for the non-normal data, my pattern of results changes.

I don't think we know and a research study is probably called for regarding "how adequate MLR is in handling missing AND non-normal data with categorical and continuous endogenous observed variables for a multilevel model. "

1. You mentioned that MLR acts like FIML in assuming normality in missing data. Does it mean that my estimator 'switches' to FIML when it deals with missing data, or is there still a difference between MLR and FIML in missing data treatment?

2. You mentioned that it is unknown whether MLR is effective in dealing with non-normal missing data. Does this apply to categorical missing data as well?

3. Would you advise if there is any other estimator that is known to effectively deal with complex (clustered) multilevel model with categorical outcome, with non-normal missing data (which may not yet be offered in MPlus)?

1. MLR is different from FIML only in how the SEs are computed, not the point estimates.

2. No, I don't think so since we only assume categorical, not a specific continuous-variable distribution.

3. None that I know of; we try to keep up with the latest. I should add that I don't worry much about the non-normal missing data case - I don't expect much of a distortion acting as if normality is the case.